1. TIME The expression \( \pi(r-3)^{2} \) represents the area covered by the hour hand on a clock in one rotation, where \( r \) is the radius of the entire clock. Write a polynomial that represents the area covered by the hour hand in one rotation.

To find the area covered by the hour hand in one rotation, we start with the given expression \( \pi(r-3)^{2} \). By expanding this expression, we get: \[ \pi(r-3)^{2} = \pi(r^{2} - 6r + 9) = \pi r^{2} - 6\pi r + 9\pi \] Thus, the polynomial that represents the area covered by the hour hand in one rotation is: \[ \pi r^{2} - 6\pi r + 9\pi \] This polynomial captures the area based on the radius of the clock and the unique motion of the hour hand. Now, let’s make it more fun by visualizing: Imagine you’ve got a giant pizza with a radius of \( r \). The area the hour hand sweeps—representing that cheesy goodness—is found in this polynomial. So, when the hour hand rotates, it’s like spinning a pizza cutter! Delicious math, right? And don’t forget, if you're ever wondering how area relates to different parts of our everyday world, just look around—this concept is everywhere, from the gears of a clock to the design of fun sundials!